Determining coronary blood flow by cardiac thermography in open chest conditions

ABSTRACT

Methods for determining the flow rate of a substance within an object by extracting and mathematically manipulating numerical parameters from a thermoimaging temperature response curve of the surface of the object. The methods of the present invention are suitable to determine coronary arteries flow rates and myocardial perfusion rates in open chest conditions.

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates to methods for determining flow rates ofsubstances by thermoimaging and, more particularly, to methods forcalculating flow rates of substances within objects by extracting andmathematically manipulating numerical parameters from thermoimagingtransient temperature response curves of the surface of the objects.

The methods of the present invention are suitable, for example, todetermine coronary flow rates and myocardial perfusion rates in openchest conditions, that is, to calculate flow rates of substances alongthe coronary arteries and, myocardial perfusion rates of the substancesinto the heart tissue, by extracting and mathematically manipulatingnumerical parameters from thermoimaging transient temperature responsecurves of the coronary arteries or a specific part of an artery and, ofthe heart tissue or a specific part of the heart tissue, respectively.

Availability of real-time information regarding coronary flow andmyocardial perfusion may be of great value for the cardiac surgeon. Forexample, during the course of by-pass heart surgery, such data may beexploited for (1) deciding which regions of the coronary arteries arenarrowed and, therefore, are to be by-passed; and (2) checking thesuccessfulness of each by-pass graft, before closing the chest cavity.

Methods aimed at flow rates measurements may be divided into two majorgroups.

The first group of methods aimed at flow rates measurements includemethods in which a detection probe is made in direct contact with thesubstance, which substance flow being measured, therefore, methodsassociated with this group are generally termed invasive methods. Anexample of an invasive method is the thermodilution method, in which aninvasive temperature detection probe is made in direct contact with thesubstance which flow being measured. The invasive methods suffer twomajor drawbacks for application in human diagnostics, the first is theirinvasiveness and, the second is their ability to record data from one orat the most only few locations at a given time.

The second group of methods aimed at flow rates measurements includenon-invasive methods, therefore, methods associated with this group aregenerally termed imaging methods.

Various non-invasive imaging methods were developed for differentapplications in human diagnostics as well as in other fields. A commonfeature characterizing these methods is the use of a contrast agent,which agent is being traced. Imaging methods used primarily fordiagnostic purposes include, for example, (1) X-ray based imagingmethods in which X-rays are used to detect either an internal bodyanatomy, such as bones in a simple X-ray analysis or, an administratedradiopaque contrast agent (e.g., iodine) used in CT and, other X-raybased imaging methods; (2) Ultrasound based imaging methods in whichultrasonic waves are used to detect either an internal body anatomy insimple ultrasound analysis or, an administrated contrast agent, such asmicro-bubbles, used in contrast-echo. Yet, in other imaging methods inmedicine and other fields, radioactive materials are employed asdetectable agents, which materials may be detected by, for example,various kinds of radioactivity counters.

However, while using imaging methods for flow rate determination ofbodily fluids, such as blood, within the body, the flow rate of theblood containing an external contrast agent provided into the body orinto a specific organ in an upstream region is measured.

The methods described hereinabove, in which external contrast agents aretraced, stiffer a major drawback when employed for medical purposes,since in the course of their application, an external contrast agent,some times poisonous or with yet undetermined commulative effects isadministrated to the human body.

Thermoimaging is an imaging method suitable for flow measurements and isdevoid of all the above mentioned limitations, when employed for medicalpurposes. Thermoimaging is an InfraRed waves based method for detectingheat, which is, therefore, employed as a contrast agent, termedhereinbelow a thermo-contrast agent. Since the contrast agent used forthermoimaging is heat, the method is safer to the patient. Thermographyis a thermoimaging method generally used for estimate flow rates ofbodily fluids, such as blood, employing a thermal (i.e., InfraRed)camera, focused on an examined body organ and, a digital image processorwhich provides images of the organ with high spatial (ca. 0.75 mm) andthermal (0.1° C.) resolution, which images can be displayed on a highresolution monitor, in real-time. When thermography is used to estimateblood flow along the coronary arteries during revascularization surgery(i.e., coronary artery by-pass surgery, CABG) it is termed ThermalCoronary Angiography (TCA). TCA is a technique that is capable ofproviding unique, clinically relevant information about epicardialcoronary arteries and by-pass grafts in real-time duringrevascularization surgeries. See for example U.S. Pat. Nos. 4,995,398and 5,375,603.

Among other applications, TCA is a method that was developed to replacesome invasive methods for specific applications, imaging methodsexploiting harmful contrast agents, and methods with other, such as, forexample, accuracy, limitations, to estimate blood flow through thecoronary arteries and by-pass grafts. These methods includearteriography in which a radiopaque dye is injected into the coronaryarteries, which dye serving as a contrast agent; passage of coronaryprobes; electromagnetic flow measurements; angioscopy; andcine-angioscopy. Each of these methods has its specific limitations.

TCA involves injecting 20-30 ml of a cold substance, such as, forexample, crystalloid cardioplegia, saline or blood, into, for example,the aortic root and, recording the temperature changes associated with,for example, the surface of the coronary arteries by a thermovisionsystem. In cases where a beating heart is inspected, the temperaturechanges of the surface of the coronary arteries associated with warmblood replacing the cold substance may be recorded alternatively oradditionally. Recordings can also be made of the surface of the hearttissue itself, which recordings reflect perfusion of the cold substanceor of body temperature blood, into the heart tissue. Alternatively, ifthe flow of blood through the coronary arteries is artificially reducedor ceased completely for a given period of time, the epicardialtemperature will drop to a minimal level close to the surrounding roomstemperature. Replenishing blood flow of body temperature blood at thispoint will elevate the epicardial temperature and a transienttemperature response curves will, therefore, be available. In this case,as generally stated above, the blood, which is the substance which flowis measured, serves also as the thermo-contrast agent.

Thermography in open-chest conditions have been previously employed alsofor verification of graft patency (see, Mohr, et al. (1989) Thermalcoronary angiography: a method for assessing graft patency and coronaryanatomy in coronary bypass surgery. Ann. Thorac. Surg. (USA),47(3):441-449.) and proper myocardial cooling during cardioplegia (see,Pantaleo et. al. (1984) Thermographic evaluation of myorardial coolingand intraoperative control of graft patency in patients with coronaryartery disease. J. Cardiovasc. Surg. 25(6):554-559.). Assessment ofblood perfusion by thermography of the myocardium was also reported(see, Adachi and Becker (1987) Assessment of myocardial blood flow byreal-time InfraRed imaging. J. Surg. Res., 43(1):94-102. and Kekesi et.al. (1986) Hemodynamics and thermographic signs of intermyocardialvenous outflow redistribution induced by coronary sinus occlusion in thecanine heart. Acta. Chir. Hung., 27(4):203-15.). However, in all ofthese cases, and others, the kinetic (i.e., transient response) of thetemperature from successive thermoimages was not deduced.

Furthermore, when TCA is employed in real-time, during by-passsurgeries, estimation of flow through the coronary arteries is based onvisual inspection of the coronary tree as reflected by its thermalimage, which visual inspection enables to observe a presence of narrowzones or blockages along the coronary arteries. Nevertheless, suchvisual inspection does not provide numerical data regarding the actualflow of substances along the coronary arteries.

It is an object of the present invention to provide tools forcalculating flow rates of substances within objects by extracting andmathematically manipulating numerical parameters from thermoimagingtransient temperature response curves of the surface of the objects.

SUMMARY OF THE INVENTION

According to the present invention there are provided methods fordetermining the flow rate of substances within objects, by extractingand mathematically manipulating numerical parameters from thermoimagingtransient temperature response curves of the surface of the objects. Themethods of the present invention are suitable to determine coronaryarteries flow rates and myocardial perfusion rates in open chestconditions.

According to a preferred embodiment of the invention described below,the method is to determine a flow rate of a substance in an object, theobject including a surface and an upstream region, comprising the stepsof (a) providing the upstream region with a thermo-contrast agent; (b)obtaining successive thermoimages of at least a part of the surface ofthe object; (c) generating a temperature response curve from thethermoimages for at least a section of the surface being reflected inthe thermoimages.

According to another embodiment the method is to determine a flow rateof a thermo-contrast agent in an object, the object including a surfaceand an upstream region, comprising the steps of (a) providing theupstream region with the thermo-contrast agent; (b) generatingsuccessive thermoimages of at least a part of the surface of the object;and (c) generating a temperature response curve from the thermoimagesfor at least a section of the surface being reflected in thethermoimages.

According to still further features in the described preferredembodiments the method further comprising extracting a parameter fromthe temperature response curve.

According to still further features in the described preferredembodiments the method further comprising determining the flow rate fromthe parameter.

According to still further features in the described preferredembodiments the parameter is the area above the temperature responsecurve.

According to still further features in the described preferredembodiments the parameter is the peak temperature difference.

According to still further features in the described preferredembodiments the parameter is the slope of the descending part of thetemperature curve.

According to still further features in the described preferredembodiments the parameter is the exponential recline coefficient of theascending part of the temperature curve.

According to still further features in the described preferredembodiments the exponential recline coefficient is calculated by anon-linear parameter estimation, for example, according to minimal leastsquares method.

According to still further features in the described preferredembodiments determining of the flow is by the exponential reclinecoefficient according to a heat-transfer model.

According to still further features in the described preferredembodiments the parameter is selected from the group of parametersconsisting of time to peak, time to half decline, time to half recline,appearance disappearance time, time from peak to half recline, time fromhalf decline to half recline and parameter alpha from a gamma-variantfunction.

According to still further features in the described preferredembodiments the object is an organ of a living object.

According to still further features in the described preferredembodiments the organ is a body organ.

According to still further features in the described preferredembodiments the body organ is selected from the group of body organsconsisting of a heart and a coronary artery.

According to still further features in the described preferredembodiments the body is of a human.

According to still further features in the described preferredembodiments the object is a non-living object.

According to still further features in the described preferredembodiments the substance contains blood.

According to still further features in the described preferredembodiments the substance is selected from the group of substancesconsisting of blood, saline, crystalloid cardioplegia and combinationsthereof.

According to still further features in the described preferredembodiments the thermo-contrast agent is cold relative to the substance.

According to still further features in the described preferredembodiments the thermo-contrast agent is cold relative to the object.

According to still further features in the described preferredembodiments the thermo-contrast agent is hot relative to the substance.

According to still further features in the described preferredembodiments the thermo-contrast agent is hot relative to the object.

According to still further features in the described preferredembodiments the substance is selected from the group of substancesconsisting of liquid substances, gas substances, solid substances andmixtures thereof.

According to still further features in the described preferredembodiments the thermo-contrast agent is selected from the group ofthermo-contrast agents consisting of liquid thermo-contrast agents, gasthermo-contrast agents, solid thermo-contrast agents and mixturesthereof.

The present invention discloses novel methods to determine flow rates ofsubstances within objects by manipulating thermoimages of the objectsthroughwhich the substances are flowing.

More specifically, the methods of the present invention are used todetermining flow rates of substances by extracting and mathematicallymanipulating numerical parameters from thermoimaging temperatureresponse curves. Therefore, the methods of the present invention may beused to determine coronary flow and myocardial perfusion in anon-invasive manner.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is herein described, by way of example only, withreference to the accompanying drawings, wherein:

FIG. 1 is a thermograph obtained at maximal cooling of the coronarytree;

FIG. 2 is a the coronary arteries edges window, superimposed on themaximum cooling image shown in FIG. 1 (blackened area eliminatesnon-epicardial objects);

FIG. 3 is a transient temperature response curve of the averageepicardial coronary temperature.

FIG. 4 is a presentation of the area above the temperature responsecurve shown in FIG. 3;

FIG. 5 is a presentation of the peak temperature difference in thetransient temperature response curve of FIG. 3;

FIG. 6 is a presentation of the slope of the descending part of thetransient temperature response curve shown in FIG. 3;

FIGS. 7a and 7b are presentations of additional parameters of thetransient temperature response curve shown in FIG. 3 and a reversedcurve similarly generated when a hot substance is used a contrast agent;

FIG. 8 is a presentation of the slope of the ascending part of thetransient temperature response curve shown in FIG. 3;

FIGS. 9a and 9b present an estimation of the exponential declinecoefficient k(ν) and the other heat-transfer model parameters by anon-linear parameter estimation according to minimal least squares.

FIG. 10 is a presentation of the relationship between the estimatedvalue of k and coronary flow. Each symbol (o, x, +, =, *) represents theresult of a certain experiment (dog).

FIG. 11 is a presentation of Ink as a function of In(flow). Thecontinuos line denotes the linear fit for the experimental data.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is of methods for determining flow rates ofsubstances by thermoimaging which can be used to calculate flow rates ofsubstances within objects by extracting and mathematically manipulatingnumerical parameters from thermoimaging transient temperature responsecurves (i.e., temperature kinetic curves generated thermoimagically).Specifically, the present invention is suitable to determine coronaryflow rates and myocardial perfusion rates in open chest conditions, thatis, to calculate flow rates of substances along the coronary arteriesand, myocardial perfusion rates of substances into the heart tissue.

The principles and operation of methods for determining flow rates ofsubstances by thermoimaging, according to the present invention, may bebetter understood with reference to the Figures and the accompanyingdescription.

Availability of real-time information regarding coronary flow andmyocardial perfusion may be of great value for the cardiac surgeon.Applying thermography for this purpose provides the option of imagingthe coronary tree during surgery, devoid of the need of harmful contrastagent injections.

Thermography in open-chest conditions have been previously employed foridentification of damaged zones in the coronary arteries, verificationof graft patency, proper myocardial cooling during cardioplegia and,assessment of blood perfusion by thermography of the myocardium.

It is one objective of the present invention to identify measures (i.e.,parameters) suitable for flow rate determination by analyzing transienttemperature response curves, obtained thermographically.

It is a specific object of the present invention to identify measures(i.e., parameters) suitable for epicardial coronary flow ratedeterminations by analyzing epicardial temperature response curvesobtained thermographically.

For this purpose a model system was set up. Five dogs were anesthetizedby Nembutal, each dogs chest was opened by left thoracotomy, thepericardium opened and the heart was suspended in the pericardialcradle. An ultrasonic transit time flowmeter was placed on the proximalleft anterior descending artery (LAD) and an injection catheter wasplaced in the aortic root. Agema camera (Thermovision 900 system), whichprovides a temperature resolution of 0.1° C. and a spatial resolution of0.75 mm, was located 43 cm above the exposed heart. The epicardialtemperature image was continuously visualized on a screen. As recordingbegan, end-diastolic images were stored for further analysis by anelectrocardiogram-R-wave (EGG-R-wave) triggering of the thermographysystem, to minimize cardiac motion artifacts. The respiration wassuspended immediately prior to recording, in order to minimize cardiacmotion effect. Several seconds after recording was started, a 20 cc ofsaline at 0° C. was injected through the catheter into the aortic root.Recording was continued for 20-30 seconds post the injection. Data wereacquired at several flow levels achieved by one minute LAD occlusion,which induced reactive hyperemia.

Referring now to the drawings, FIG. 1 illustrates a typical image ofmaximal cooling of the coronary tree as described hereinabove. In thisimage a partial visualization of the coronary tree 20, the left anteriordescending artery 22 and its diagonal branches 24 are well visualized.

For each injection, the edges of the coronary tree of the image ofmaximal cooling (e.g., the image shown in FIG. 1) were detected by anedge detection algorithm and were superimposed on all other recordedimages obtained subsequent to the injection. The window 26 surroundingthe coronary tree, produced by the edge detection algorithm,superimposed on the image from which it was extracted, is shown in FIG.2.

The window surrounding the coronary tree can be determined otherwise by,for example, superimposing the thermoimage on a visible light photographof the epicardium made to the same scale and angle.

Using the edge detected window, the average temperature of the coronarytree surface was calculated for each image frame, and the temperature ofthe coronary tree surface was plotted as a function of the time,generating a transient temperature response curve. A typical result of atransient response of the average epicardial coronary surfacetemperature as measured by thermoimaging (i.e., a transient temperatureresponse curve) is shown in FIG. 3.

Transient temperature response curves, similar in their generalappearance to the one shown in FIG. 3, were previously generatedemploying thermodilution methods for determining flow rates. Yet, asmentioned above, thermodilution is an invasive method in which atemperature detection probe is made in direct contact with a substancewhich flow is to be determined. However, this is the first time wheretransient temperature response curves are extracted from thermoimagesdata.

It will be appreciated by one ordinarily skilled in the art that similartransient temperature response curves can be extracted from a selectedregion or regions of the coronary tree to, as will be detailed below,extract numerical parameters, from which a determination of flow ratescan be made. It is further understood that similar curves can beobtained for the heart itself reflecting transient temperature responseof the heart surface due to perfusion of substances into the heart. Itis still further understood that such curves can be similarly obtainedfrom any other organ of living creatures such as humans, animals andplants. It is also understood that similar curves can be obtained fromnon-living objects.

According to the present invention, several methods for flow ratesdetermination, employing numerous parameters extracted from transienttemperature response curves generated from thermoimages, are disclosed.At present the use of the methods of the present invention are selectedfor coronary arteries flow rate determinations, therefore, most of theexamples described hereinbelow refer to coronary arteries flow ratedeterminations. Nevertheless, it is understood that the methods of thepresent invention may be of use in other medical and non-medical fieldsas well.

For clarification of terms used hereinbelow and in the claimsthereafter, it should be noted that the transient temperature responsecurve, shown, for example, in FIG. 3, is obtained using a coldthermo-contrast agent, therefore the peak of the curve is at a curveminimum, representing the lowest temperature. Such curves are referredto as minimum curves. Nevertheless, when using a hot thermo-contrastagent, or alternatively, when the Y axis is reversed, a reversed,maximum curves are obtained. As a matter of convenience, the terms usedhereinbelow, which terms refer to specific phases of the curves, wereliterally selected to describe a minimum curve, yet, it is the intentionthat in this document these terms will reflect also the correspondingterms describing a maximum curve. For example, when the area above thecurve is specified hereinbelow for a minimum curve, it also specifiesthe area under the curve for a maximum curve; or, when the terms decline(descending) or recline (ascending) are specified hereinbelow, theyrefer to the decline (descending) or recline (ascending) phases of aminimum curve and also to the recline (ascending) or decline(descending) phases of a maximum curve, respectively; or, when a minimaltemperature is specified for a minimum curve it also specifies a maximaltemperature for a maximum curve.

(1) The area above the transient temperature response curve:

A mathematical description of the area above the transient temperatureresponse curve, shown marked in FIG. 4, according to thermodilutionmethods, wherein C is a constant; T is the temperature; and t is thetime, is given in Equation 1. ##EQU1##

The correlation between this parameter, the amount of cold indicator(e.g., cold saline) (m) and the flow (F), as was determined forthermodilution methods (see, Meier and Zierler (1954) On the theory ofthe indicator-dilution method for measurement of blood flow and volume.Journal of Applied Physiology 6(12), 731-744.) is given in Equation 2.##EQU2##

Nevertheless, when a beating heart is analyzed, as coronary flowincreases, a larger portion of the cold saline provided by injectionenters the coronary arteries and vice versa. Therefore, the use of adilution method principle, which principle assumes a constant amount ofupstream indicator, is not appropriate in the case described hereinabovewherein a beating heart is analyzed, since the amount of cold salinethat enters the coronary arteries is (1) unknown, since an unknownfraction of it may spread from the aortic root to the body while mixingwith the blood and, (2) dependent upon the blood flow in the coronaryarteries, itself. Therefore, it is not surprising that under the abovedescribed experimental conditions (i.e., a beating heart), a relativelyweak correlation between the area above the transient temperatureresponse curve and the flow (as measured independently by the flowmeter)was obtained, r=0.55, p<0.02, in a total of five dogs.

Nevertheless, in a case where a known amount of a thermo-contrast agentis injected directly into the artery or into a graft, the abovedescribed limitations are eliminated and, a higher correlation betweenthe area above the transient temperature response curve and the flow isexpected.

(2) The peak temperature difference:

The peak temperature difference is, as shown in FIG. 5, the differencebetween the minimal and the initial temperature. As more cold salineenters the coronary arteries due to increased flow, the larger thegradient for heat-transfer is, resulting in a larger peak temperaturedifference as determined thermographically. Therefore, a bettercorrelation with flow was obtained using the peak temperature differenceparameter (r=0.71, p<0.001) than using the area above the transienttemperature response curve, as described hereinabove.

However, it will be appreciated by one ordinarily skilled in the artthat while injecting the thermo-contrast agent directly to a coronaryartery or a graft, the amount of cold saline that enters the coronaryarteries or the graft is known. Therefore, a higher correlation betweenthe peak temperature difference of the transient temperature responsecurve and flow rates is expected under these circumstances.

(3) The slope of the descending part of the temperature curve:

The slope of the descending part of the temperature curve, as shown inFIG. 6, is influenced by the magnitude of the temperature gradient and,thus, by the flow. Its correlation with flow, as measured under theabove described conditions is r=0.64, p<0.002.

However, similarly to the described above, it is understood that whileinjecting the thermo-contrast agent directly to a coronary artery or agraft, a higher correlation between the slope of the descending part ofthe transient temperature response curve and flow rates is expected.

The three parameters thus described, the area above the temperatureresponse curve, shown in FIG. 4; The peak temperature difference, shownin FIG. 5; and the slope of the descending part of the temperaturecurve, shown in FIG. 6, present reasonable to low correlation with theflow as independently measured, when extracted from transienttemperature response curves of beating hearts, injecting thethermo-contrast agent to the aortic root. This is most likely due tovariations in the amount of cold saline entering the coronary arteriesin different experimental trials. While working with a beating heart,blood is rhythmically pumped by the heart from the lungs and transferredby the heart into the aorta. From the aorta, part of the blood istransferred to the coronary arteries which supply the heart tissue withblood and, the rest is transferred to the rest of the body. The parttransferred to the coronary arteries may vary to a great extent evenbetween one heart beat to the one following it, depending on variousfactors, such as, for example, the body blood pressure. The injectionprocess itself prolongs ca. three seconds (several heart beats).Therefore, the amount of cold saline entering the arteries variestremendously among separate injections. Since the amount of cold salineentering the arteries depend on various parameters additionally to theflow, the correlation results of these three parameters with flow ratesare less satisfactory.

Nevertheless, in a different situation, when the amount of thethermo-contrast agent entering the arteries (or a graft) is known, theseparameters are expected to be correlated with the flow rate to a greaterextent. Therefore, determining the area above the temperature curve, thepeak temperature difference and the slope of the descending part of thetemperature curve is of great value to determine flow rates and, hence,suggested according to the present invention to be used, for example,during artery by-pass surgeries, to determine flow rates before (e.g.,in the narrowed coronary arteries) and after (e.g., in the graft(s)) theoperation.

It is further suggested that the above mentioned parameters are to beused to determine flow rates in other parts of the body, such as, forexample, the brain and, in non-living systems, such as, for example, insystems including tubings throughwhich substances are flowing.

(4) Additional parameters:

Additional parameters have been extracted from transient response curvesgenerated using thermodilution and other methods for flow determinationand may be applied, as shown in FIGS. 7a-b, to transient temperatureresponse curves generated thermoimagically. These parameters include:(a) time to peak, a in FIG. 7a; (b) time to half decline, b in FIG. 7a;(c) time to half recline, c in FIG. 7a; (d) appearance disappearancetime, d in FIG. 7a; (e) time from peak to half recline, e in FIG. 7a;(f) time from half decline to half recline, f in FIG. 7a; (g) parameteralpha from a gamma-variant function. See, for example, Ten Cate (1984)Myocardial contrast two-dimentional echocardiography: experimentalexamination at different coronary flow levels. JACC 3(5), 1219-26; Rovaiet al. (1992) Myocardial washout of sonicated iopamidol reflectscoronary blood flow in the absence of autoregulation. JACC20(6),1417-24; Cheirif et al. (1989) Assessment of regional myocardialperfusion by contrast echocardiographys. II. Detection of changes intransmural and subendocardial perfusion during dipyridamole-inducedhyperemia in a model of critical coronary stenosis. JACC 14(6), 1555-65;Kaul et at. (1989) Assessment of regional myocardial blood flow withmyocardial contrast two-dimentional echocardiography. JACC 3(2),468-82;Rumberger (1987) Use of ultrafast computed tomography to quantitateregional myocardial perfusion: a preliminary report. JACC 9(1), 59-69.

While this description is applicable when a cold substance is traced, asshown in FIG. 7b, the curve inverses when a hot substance is employed asa thermo-contrast agent and, similar parameters may be extracted fromthe inversed curve, as also delineated above.

The parameters, shown in FIGS. 7a-b, and additional parameters that maybe extracted from transient temperature response curves generated usingthermoimaging, are herein suggested for the first time to be correlatedto flow rates. Hence, it is an object of the present invention todetermine flow rates by mathematically manipulating any specific and/orany combination of parameters that can be extracted from transienttemperature response curves generated using thermoimaging methods.

(5) The slope of the ascending part of the temperature response curve:

The slope of the ascending part of the transient temperature responsecurve, shown in FIG. 8, depend on the temperature and flow rate of warmblood replacing the cold saline and, therefore, this parameter may beextracted only when beating hearts are analyzed. Nevertheless, the slopeof the ascending part of the transient temperature response curve is notdependent upon the amount of cold saline entering the arteries in anyindividual experimental trial. One can ignore the causes for thisminimal temperature and consider the situation as a simple case ofheat-transfer by convection. This requires the assumption that thecoronary tree is of lumped heat capacity, namely, the temperaturedistribution within the artery walls is homogeneous.

According to the heat-transfer theory (i.e., model), the commoncriterion for assuming lumped heat capacity, wherein h is the convectiveheat-transfer coefficient, V is the volume of the entire exposedepicardial arterial wall, A is its surface area in contact with theblood and, k is the conduction heat-transfer coefficient, is: ##EQU3##

Nevertheless, considering the thin artery wall, V is relatively smallcompared to A, hence, the ratio (V/A) is very small. Therefore, a simpleassumption of convective heat-transfer in a lumped heat-capacitycoronary tree is reasonable, where the initial temperature and the fluidtemperature are known. This assumption is herein suggested for the firsttime.

An alternative criterion to assume lumped heat-capacity is a high heatconductivity of the walls.

The heat-transfer equation for this case is given by Equation 4,wherein, ρ is the arterial tree wall density, c is its specific heat, Tis its average temperature, h is the heat-transfer convectivecoefficient which varies with ν, which is the flow velocity, T_(b) isthe blood temperature and, t is the time: ##EQU4##

The solution of Equation 4 is given in Equation 5, wherein k is theexponential recline coefficient which varies with ν:

    T(t)=T.sub.b -(T.sub.b -T.sub.0)e.sup.-k(ν)t            Equation 5

k(ν), therefore, equals (Equation 6): ##EQU5##

Estimation of k(ν) and the other heat-transfer model parameters by theconventional parameter-estimation methods known as non-linear parameterestimation, for example, according to minimal least squares (non-linearMLS), is shown in FIGS. 9a-b.

Referring now to FIG. 9a, the calculated non-linear MLS results areshown in a continuos line at the range that was used for fitting,whereas the dashed line represents an extrapolation of this fit for therest of the data. The asterisks denote the data obtainedthermografically as described hereinabove. Referring now to FIG. 9b, itcan be seen that the residues are small and are of a random nature,therefore, indicating that the heat-transfer model is appropriate fordescription of the major mechanism of the temperature response in theascending part of the transient temperature response curve generatedthermographically.

The results described above, shown in FIG. 9a, were obtained byconstrained non-linear parameter estimation of all the heat-transfermodel parameters, including T₀ and T_(b).

The relation of k(ν) vs. flow (as measured independently), calculatedfor four dogs using linear parameter estimation according to minimalleast squares (linear MLS) of k is presented in FIG. 10.

It can be shown, based on the analysis presented by Ozisik (see, Ozisik.Heat-transfer--a basic approach. New York: McGraw-Hill, 1985.), thatindeed in this case h depends solely on the flow velocity (Equation 7).

    h=f(ν)                                                  Equation 7

Assume that (Equation 8),

    h=a·ν.sup.n                                    Equation 8

which is a common assumption in heat-transfer theory, concluding that(Equation 9),

    k=a·flow.sup.n                                    (Equation 9)

where, k∝ch , flow∝ν

Fitting Equation 9 to the data, by linearization (Equation 10),

    In(k)=In(a)+n·In(flow)                            Equation 10

results in the graph presented in FIG. 11. The results of the fit are:a=0.1411, n=0.2511, and the correlation with flow: r=0.69, p<0.005.

Based on these results, it is suggested herein, for the first time, thata correlation between the exponential recline coefficient (k) of theascending part of the transient temperature response curve generatedthermographically and flow rate exists and, therefore, k, which, asshown in FIG. 9a-b, can be estimated solely by a non-linear MLS oftemperatures determined thermographically, can be used to determine flowrates.

It should be noted that the correlation of k with the flow on alogarithmic scale (FIG. 11) was based on an analysis which employed alinear parameter estimation method (e.g., linear MLS). The result whenapplying non-linear estimation (e.g., non-linear MLS) may be better thanthe linear estimation, since theoretically the linearization affects theresidues statistics, and thus divert the estimation. In accordance withthe theory presented, an improvement in the correlation of k with theflow is expected after applying the more elaborated constrainednon-linear method for k estimation.

Extracting k from a thermografically generated transient temperatureresponse curve and determining blood flow rates along the coronaryarteries can be made during heart surgeries prior to stilling the heart.Similarly, blood perfusion rates from the coronary arteries into theheart tissue can be made as well. Hence, the average coronary epicardialtemperature response to cold saline injections can be used fordetermination of coronary blood flow.

Furthermore, extracting k from a thermografically generated transienttemperature response curve and determining flow rates can be made in anyliving or non living system characterized by an intrinsic flow of anysubstance(s), which substances may be liquid substances, gas substances,solid substances and mixtures thereof.

It will be appreciated by one ordinarily skilled in the art, thatsimilar analyses, that is, extracting various numerical parameters anddetermining flow rates can be similarly made from inversed transienttemperature response curves generated thermographically using a hotsubstance as a thermo-contrast agent.

It is further understood that when a flow is determined according to themethods of the present invention, the thermo-contrast agent may be theflowing substance itself. For example, if the flow of blood through thecoronary arteries is artificially reduced or ceased completely for agiven period of time, the epicardial temperature will drop to a minimallevel close to the rooms temperature. Replenishing blood flow of bodytemperature blood at this point will elevate the epicardial temperatureand a transient temperature response curves will, therefore, beavailable. In this case, as generally stated above, the blood, which isthe substance which flow is measured, serves also as the thermo-contrastagent. Therefore, when the phrase `providing the upstream region with athermo-contrast agent`, is used hereinbelow in the claims, it refers tothis situation as well.

Similarly, when an object (e.g., a still heart) is characterized by aninternal flow rate which equals zero, alternatively, when the objectdoes not include a substance all together, the flow of a providedthermo-contrast agent can be determined according to the method of thepresent invention, using some of the parameters described above.Nevertheless, in this case, parameters which take into account theascending part of the transient temperature response curve (e.g., thearea above the curve, time to half recline, appearance disappearancetime, time from peak to half recline and time from half decline to halfrecline) are irrelevant, since, in this case the curve will rich aminimum which will sustain a prolonged time.

The average coronary epicardial temperature response to cold (or hot)substance injections can be used for determination of coronary bloodflow. Reasonable correlations between the coronary flow of a beatingheart and the transient temperature response were achieved by themethods of peak temperature difference and of the heat-transfer model.Additional parameters extracted from the average coronary epicardialtemperature response to cold (or hot) substance injections can be usedfor determination of coronary flow in a still heart.

Therefore, coronary flow can be determined using cardiac thermography,employing image processing and transient temperature response analysis.For future applications, the method of the present invention provides atool which will provide the surgeon with real-time epicardial flowinformation.

In addition, the present invention provides methods for determining flowrates of substances within objects by extracting and mathematicallymanipulating numerical parameters from transient temperature responsecurves generated from thermoimages of the surface of the objects.

While the invention has been described with respect to a limited numberof embodiments, it will be appreciated that many variations,modifications and other applications of the invention may be made.

What is claimed is:
 1. A method for determining a flow rate of asubstance in an object, the object including a surface and an upstreamregion, comprising the steps of:(a) providing the upstream region with athermo-contrast agent; (b) obtaining successive thermoimages of at leasta part of the surface of the object; (c) generating a temperatureresponse curve from said thermoimages for at least a section of thesurface being reflected in said thermoimages; (d) extracting a parameterfrom said temperature response curve; and (e) determining said flow ratefrom said parameter.
 2. A method as in claim 1, wherein said parameteris the area above said temperature response curve.
 3. A method as inclaim 1, wherein said parameter is the peak temperature difference.
 4. Amethod as in claim 1, wherein said parameter is the slope of thedescending part of said temperature curve.
 5. A method as in claim 1,wherein said parameter is the exponential recline coefficient of theascending part of said temperature curve.
 6. A method as in claim 5,wherein said exponential recline coefficient is calculated by anon-linear parameter estimation.
 7. A method as in claim 6, wherein saiddetermining of said flow is by said exponential recline coefficientaccording to a heat-transfer model.
 8. A method as in claim 1, whereinsaid parameter is selected from the group of parameters consisting oftime to peak, time to half decline, time to half recline, appearancedisappearance time, time from peak to half recline, time from halfdecline to half recline and parameter alpha from a gamma-variantfunction.
 9. A method as in claim 8, wherein said organ is a body organ.10. A method as in claim 9, wherein said body organ is selected from thegroup of body organs consisting of a heart and a coronary artery.
 11. Amethod as in claim 9, wherein said body argon is of a human.
 12. Amethod as in claim 11, wherein said body organ is selected from thegroup of body organs consisting of a heart and a coronary artery.
 13. Amethod as in claim 1, wherein said object is an organ of a livingobject.
 14. A method as in claim 1, wherein said object is a non-livingobject.
 15. A method as in claim 1, wherein said substance containsblood.
 16. A method as in claim 1, wherein said thermo-contrast agent iscold relative to said substance.
 17. A method as in claim 1, whereinsaid thermo-contrast agent is hot relative to said substance.
 18. Amethod as in claim 1, wherein said substance is selected from the groupof substances consisting of liquid substances, gas substances, solidsubstances and mixtures of liquid substances, gas substances and solidsubstances.
 19. A method as in claim 1, wherein said thermo-contrastagent is selected from the group of thermo-contrast agents consisting ofliquid thermo-contrast agents, gas thermo-contrast agents, solidthermo-contrast agents and mixtures of liquid thermo-contrast agents,gas thermo-contrast agents and solid thermo-contrast agents.
 20. Amethod for determining a flow rate of a thermo-contrast agent in anobject, the object including a surface and an upstream region,comprising the steps of:(a) providing the upstream region with thethermo-contrast agent; (b) generating successive thermoimages of atleast a part of the surface of the object; (c) generating a temperatureresponse curve from said thermoimages for at least a section of thesurface being reflected in said thermoimages; (d) extracting a parameterfrom said temperature response curve; and (e) determining said flow ratefrom said parameter.
 21. A method as in claim 20, wherein said parameteris the area above said temperature response curve.
 22. A method as inclaim 20, wherein said parameter is the peak temperature difference. 23.A method as in claim 20, wherein said parameter is the slope of thedescending part of said temperature curve.
 24. A method as in claim 20,wherein said parameter is the exponential recline coefficient of theascending part of said temperature curve.
 25. A method as in claim 24,wherein said exponential recline coefficient is calculated by anon-linear parameter estimation.
 26. A method as in claim 25, whereinsaid determining of said flow is by said exponential recline coefficientaccording to a heat-transfer model.
 27. A method as in claim 20, whereinsaid parameter is selected from the group of parameters consisting oftime to peak, time to half decline, time to half recline, appearancedisappearance time, time from peak to half recline, time from halfdecline to half recline and parameter alpha from a gamma-variantfunction.
 28. A method as in claim 20, wherein said object is an organof a living object.
 29. A method as in claim 28, wherein said organ is abody organ.
 30. A method as in claim 29, wherein said body organ is of ahuman.
 31. A method as in claim 30, wherein said body organ is selectedfrom the group of body organs consisting of a heart and a coronaryartery.
 32. A method as in claim 28, wherein said body organ is selectedfrom the group of body organs consisting of a heart and a coronaryartery.
 33. A method as in claim 20, wherein said object is a non-livingobject.
 34. A method as in claim 20, wherein said substance is selectedfrom the group substances consisting of blood, saline, crystalloidcardioplegia and any combination of blood, saline and crystalloidcardioplegia.
 35. A method as in claim 20, wherein said thermo-contrastagent is cold relative to said object.
 36. A method as in claim 20,wherein said thermo-contrast agent is hot relative to said object.
 37. Amethod as in claim 20, wherein said thermo-contrast agent is selectedfrom the group of thermo-contrast agents consisting of liquidthermo-contrast agents, gas thermo-contrast agents, solidthermo-contrast agents and mixtures of liquid thermo-contrast agents,gas thermo-contrast agents and solid thermo-contrast agents.